I haven't been involved in audio for a long time -- years of living in poverty will do that to ya...but I am slowly starting to get involved again.
One thing I learned 40 years ago is that wire gauge DOES make a difference with how speaker wires effect sound.
Here's how it started: At the time, I had just read an article on speakers and damping factor. (FYI, damping factor is the ratio of the speaker impedance to the output impedance of the power amp.) Power amps with a lower output impedance will increase the damping factor at the loudspeaker which improves the control that the amp has over moving the speaker's diaphragms. The lower the damping factor, the less control the power amp has over the speaker; the higher the damping factor, the more control the amplifier has over the speaker system. There's just one problem: the DC resistance of the cable between the speaker and the power amp can effect the damping factor.
After reading the article, I realized that the resistance of the connecting wire could have an effect on the sound if the resistance was significant. So I decided to try an experiment. At the time I was using 15' lengths of 18 gauge zip (lamp) cord for my speaker cables. It has a series resistance of .1 ohm per lead. I replaced it with 12 gauge wire cut to the length between the speakers and power amp - 7'. This has a series resistance of .01 ohm per lead - 1/10 that of the zip cord.
When I started listening to music with the new cables, my initial reaction was: "Where did all the bass go?" Suddenly my loudspeakers sounded bass shy, whereas they had sounded deeper and fuller with the thinner cables. After a little thought I understood what had happened: the series resistance of the wire not only affects the damping factor but also the Qtc of the speaker system. Increasing the resistance increases the Qtc, which creates a boost in the low bass and lowers the F3 of the system. Assuming my power amp had an output impedance of .05 ohm (not unusual for a solid state power amp), with the 18 gauge wire the damping factor was 8 / .05+.1+.1 ohms = a DF of 32. with the 12 gauge wire the DF increased to 114 a factor close to 4X what it previously was. I don't know anymore how it it affected the Qtc (I don't remember the math for that -- remember, it HAS BEEN 40 years!) but the difference was clearly audible. Once I listened to the system for a greater length of time, I realized that some of the low bass was missing, but on the other hand, the bass that was there sounded much tighter and had a lot more "punch" -- something that would definitely be affected by an increase in damping factor.
There were no "magic" or expensive cables involved, just something with a heavier gauge and lower resistance. FYI, if you twist both leads of a pair of wires together that are the same wire gauge, you decrease the gauge size by 2. Therefore two 16 gauge wires twisted together is the same as a single 14 gauge wire. Two 14's are the same as a 12 gauge and so on.
I hope this helps.